Murty’s ranking algorithm provides a clever way of partitioning the solution space to find the M best assignments, whose costs are in a nondecreasing order, to a linear assignment problem with an N N cost matrix, where total assignment cost is minimized. This paper reviews the optimization techniques for Murty’s M -best method combined with successive shortest path assignment algorithms (such as the Jonker and Volgenant assignment algorithm) from two papers. The first paper discussed three optimizations: 1) inheriting dual variables and partial solutions during partitioning, 2) sorting subproblems by lower cost bounds before solving, and 3) partitioning in an optimized order. The second paper proposed updating the dual variables of the previous solution before the shortest path procedure is applied to solve a subproblem without mentioning the use of lower cost bounds. One contribution of this paper is that we propose a much tighter lower bound than that given by the first paper. Comparative tests have been conducted among algorithms employing different combinations of the optimization techniques to evaluate their respective performances.
This paper considers the localization of a point target from an optical sensor's focal plane array (FPA) with a dead zone separating neighboring pixels. The Cramer Rao lower bound (CRLB) for the covariance of the maximum likelihood estimate (MLE) of target location is derived based on the assumptions that the energy density of the target deposited in the FPA conforms to a Gaussian point spread function (PSF) and that the pixel noise is based on a Poisson model (i.e., the mean and variance in each pixel are proportional to the pixel area), . Extensive simulation results are provided to demonstrate the efficiency of the MLE of the target location in the FPA. Furthermore, we investigate how the estimation performance changes with the pixel size for a given dead zone width. It is shown that that there is an optimal pixel size which minimizes the CRLB for a given dead zone width.
This paper considers the problem of estimating the 3D states of a salvo of thrusting/ballistic endo-atmospheric objects using 2D Cartesian measurements from the focal plane array (FPA) of a single fixed optical sensor. Since the initial separations in the FPA are smaller than the resolution of the sensor, this results in merged measurements in the FPA, compounding the usual false-alarm and missed-detection uncertainty. We present a two-step methodology. First, we assume a Wiener process acceleration (WPA) model for the motion of the images of the projectiles in the optical sensor’s FPA. We model the merged measurements with increased variance, and thence employ a multi-Bernoulli (MB) filter using the 2D measurements in the FPA. Second, using the set of associated measurements for each confirmed MB track, we formulate a parameter estimation problem, whose maximum likelihood estimate can be obtained via numerical search and can be used for impact point prediction. Simulation results illustrate the performance of the proposed method.
The probabilistic multiple-hypothesis tracker (PMHT), a tracking algorithm of considerable theoretical elegance based on the expectation-maximization (EM) algorithm, will be considered for the problem of multiple target tracking (MTT) with multiple sensors in clutter. Aside from position observations, continuous measurements associated with the unique and constant feature of each target are incorporated to jointly estimate the states and feature of the targets for the sake of tracking and classification, leading to a bootstrapped implementation of the PMHT. In addition, we rederived the information matrix for the big state vector stacking states for all the targets at all the time steps during the observation time. Simulation results have been conducted for both closely spaced and well separated scenarios with and without feature measurements. The normalized estimation error squared (NEES) calculated using the information matrix for both scenarios with and without feature measurements are within the 95% probability region. In other words, the estimates are consistent with the corresponding covariances.
Multiple target tracking (MTT) is a challenging task that aims to estimate the number of targets and their states in the presence of process noise, measurement noise and data association uncertainty. This paper considers a special MTT problem characterized by additional complexity. In this problem, multiple targets are launched simultaneously in nearby locations at the same speed with slightly diﬀerent directions. As the distances be-tween the initial locations of these targets are smaller than the resolution of the sensor, this results in merged measurements, i.e., unresolved tracks at the very beginning. To deal with this problem, the recently proposed Multi-Bernoulli (MB) ﬁlter is applied. Using a model for the merged measurements, simulation results with 2-D Cartesian measurements in an optical sensor’s focal plane in the presence of clutter show that the initially unresolved tracks become resolved with MB ﬁltering a few time steps after the measurements become resolved. Thus, the MB ﬁlter is capable of keeping track of the number of targets and their corresponding states when they are initially unresolved.